You certainly can sue the thief, but you will need to call the two witnesses in Court to prove the theft and you will have to testify to prove the contents of the purse. Since most people don't carry $2000 worth of valuables in their purse, the jury will also have to decide how much value they place on the contents of your purse, so you will have to convince them not only of the thief's culpability, but also of the value of the things you lost.
One thing you might not have considered is that most thieves don't have a lot of money--that's one of the reasons they steal. Many lawyers in Texas would assume that the thief probably has no money and would therefore request to be paid on an hourly basis. It's very possible that you could spend more than $2000 in attorneys fees only to get a judgment against the thief that you can't collect on--because the thief has no money.
Because the amount of attorneys fees might easily exceed the amount you lost, you might do better to handle the matter yourself by filing in small claims court. Another option would be to speak to the District Attorneys office to see if you can get restitution through the criminal justice system. Whichever route you choose, I wish you the best of luck in recovering the stolen money.